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Regularity for the one-phase Hele-Shaw problem from a Lipschitz initial surface
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 129, Number 2, April 2007
- pp. 527-582
- 10.1353/ajm.2007.0008
- Article
- Additional Information
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In this paper we show that if the Lipschitz constant of the initial free boundary is small, then for small positive time the solution is smooth and satisfies the Hele-Shaw equation in the classical sense. A key ingredient in the proof which is of independent interest is an estimate up to order of magnitude of the speed of the free boundary in terms of initial data.